Question: $ D = \left[\begin{array}{rr}2 & 0 \\ 0 & 1\end{array}\right]$ $ F = \left[\begin{array}{rr}0 & 2 \\ 4 & 3\end{array}\right]$ Is $ D- F$ defined?
Solution: In order for subtraction of two matrices to be defined, the matrices must have the same dimensions. If $ D$ is of dimension $( m \times  n)$ and $ F$ is of dimension $( p \times  q)$ , then for their difference to be defined: 1. $ m$ (number of rows in $ D$ ) must equal $ p$ (number of rows in $ F$ ) and 2. $ n$ (number of columns in $ D$ ) must equal $ q$ (number of columns in $ F$ Do $ D$ and $ F$ have the same number of rows? Yes Yes No Yes Do $ D$ and $ F$ have the same number of columns? Yes Yes No Yes Since $ D$ has the same dimensions $(2\times2)$ as $ F$ $(2\times2)$, $ D- F$ is defined.